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Definition

A comma is a small interval that occurs in just intonation, between two intervals which are close in pitch. Commas are always greater than 1 and not a power such as a square or cube of any other interval, and generally in a low prime limit. The word is often used in reference to regular tempering when the comma is tempered out, which is to say reduced to a unison, by the temperament, thereby equating the intervals separated by that comma. For example the Syntonic or Didymus comma of 81/80, which occurs between 10/9 and 9/8, as well as 81/64 and 5/4, is tempered out by meantone temperament. Commas are usually written as ratios, but they can also be written as monzos. The following lists mostly give both forms, as well as the size in cents.

For commas over 100 cents in size, see Large commas; and for commas under 3.5 cents in size, see Unnoticeable commas

List of commas, by prime limit

3-limit commas

name(s)
ratio
monzo
cents
limma, Pythagorean minor second
256 / 243
| 8 -5 >
90.225
Pythagorean comma

| -19 12 >
23.460
17-comma

| 27 -17 >
66.765
29-comma

| 46 -29 >
43.305
41-comma

| 65 -41 >
19.845
Pythagorean Integer cents comma

| 317 -200 >
9.000
Mercator's comma, 53-comma

| -84 53 >
3.615
70-comma

| 111 -70 >
63.150

5-limit commas

name(s)
ratio
monzo
cents
Twenty-two thirds limma

| -51 0 22 >
98.902
sibbolet

| -58 0 25 >
57.843
Hunt 5-cycle comma

| -65 0 28 >
16.784
acute thirds comma

| 72 0 -31 >
24.275
34-5-comma

| 79 0 -34 >
65.334
Schismic thirds chromatic semitone

| -123 0 53 >
74.627
10-15-comma

| -39 10 10 >
82.687
11-15-comma

| 43 -11 -11 >
29.044
21-15-comma

| 82 -21 -21 >
53.643
32-15-comma

| 125 -32 -32 >
24.599
Huntian 15-cycle comma

| -168 43 43 >
4.445
53-15-comma

| -207 53 53 >
78.242
54-15-comma

| 211 -54 -54 >
33.489
76-15-comma

| 297 -76 -76 >
91.578
major chroma, major limma, pelogic comma
135 / 128
| -7 3 1 >
92.179
ripple
6561 / 6250
| -1 8 -5 >
84.071
doublewide

| -9 -6 8 >
78.780
sevond

| 6 -14 7 >
76.826
nusecond

| 5 13 -11 >
75.964
sentinel

| -33 15 4 >
74.580
chromatic semitone
25 / 24
| -3 -1 2 >
70.672
superpyth, grave minor second
20480 / 19683
| 12 -9 1 >
68.719
major diesis, diminished comma
648 / 625
| 3 4 -4 >
62.565
passion

| 18 -4 -5 >
60.611
shibboleth

| -5 -10 9 >
57.273
mynic

| 9 9 -10 >
54.458
tritonic

| -29 11 5 >
53.074
negri comma, double augmentation diesis
16875 / 16384
| -14 3 4 >
51.120
maximal diesis, porcupine comma
250 / 243
| 1 -5 3 >
49.166
immunity

| 16 -13 2 >
47.212
diesis, augmented comma
128 / 125
| 7 0 -3 >
41.059
wizard

| -31 2 12 >
39.675
sycamore

| -16 -6 11 >
37.721
fifive

| -1 -14 10 >
35.767
unicorn

| -2 13 -8 >
34.905
valensixthtone

| 13 5 -9 >
32.952
ampersand, Ampersand's comma

| -25 7 6 >
31.567
small diesis, magic comma
3125 / 3072
| -10 -1 5 >
29.614
minimal diesis, tetracot comma
20000 / 19683
| 5 -9 4 >
27.660
roda

| 20 -17 3 >
25.706
maja

| -3 -23 17 >
22.368
syntonic comma, Didymos comma, meantone comma
81 / 80
| -4 4 -1 >
21.506
maquila comma

| 49 -6 -17 >
20.937
diaschisma
2048 / 2025
| 11 -4 -2 >
19.553
ditonma

| -27 -2 13 >
18.168
misty comma

| 26 -12 -3 >
17.599
pental comma

| -28 25 -5 >
17.306
graviton, gravity comma

| -13 17 -6 >
15.353
quartonic

| 3 -18 11 >
14.261
medium semicomma, sensipent comma
78732 / 78125
| 2 9 -7 >
13.399
Würschmidt comma

| 17 1 -8 >
11.445
semicomma, Fokker comma

| -21 3 7 >
10.061
escapade comma

| 32 -7 -9 >
9.492
kleisma, semicomma majeur
15625 / 15552
| -6 -5 6 >
8.107
unidecma

| -7 22 -12 >
7.245
mutt comma

| -44 -3 21 >
6.723
amity comma

| 9 -13 5 >
6.154
parakleisma

| 8 14 -13 >
5.292
gammic comma

| -29 -11 20 >
4.769
vulture comma

| 24 -21 4 >
4.200
23-3/5-comma

| 17 23 -23 >
59.750
34-3/5-comma

| -25 -34 34 >
68.196
53-3/5-comma

| 39 53 -53 >
71.012

7-limit commas

name(s)
ratio
monzo
cents
hexadecatone comma, 16-7-comma

| 45 0 0 -16 >
98.7855
21-7-comma

| 59 0 0 -21 >
54.656
Hunt 7-cycle comma

| 73 0 0 -26 >
10.526
German sixth comma

| -87 0 0 31 >
33.603
large deep red comma
6561 / 6272
| -7, 8, 0 -2 >
77.988
36-7-comma

| -101 0 0 36 >
77.737
47-7-comma

| 132 0 0 0 -47 >
65.182
slendro integer cents comma

| 1127 0 0 -400 >
69.637
29-7/5-comma

| -14 0 -29 29 >
92.854
31-7/5-comma

| -15 0 -31 31 >
57.878
33-7/5-comma

| -16 0 -33 33 >
22.902
35-7/5-comma

| 18 0 35 -35 >
12.073
37-7/5-comma

| 19 0 37 -37 >
47.049
39-7/5-comma

| 20 0 39 -39 >
82.0245
5-21-comma

| 22 -5 0 -5 >
46.0955
18-21-comma

| -79 18 0 18 >
74.056
23-21-comma

| -101 23 0 23 >
27.961
Huntian 21-cycle comma

| 123 -28 0 -28 >
18.135
33-21-comma

| 145 -33 0 -33 >
64.230
8-35-comma

| -41 0 8 8 >
41.117
15-35-comma

| 77 0 -15 -15 >
72.906
23-35-comma

| 118 0 -23 -23 >
31.789
31-35-comma

| -159 0 31 31 >
9.328
39-35-comma

| -200 0 39 39 >
50.445
47-35-comma

| -241 0 47 47 >
91.562
Huntian 35-cycle comma

| 277 0 -54 -54 >
22.4605
greenwoodma
405 / 392
| -3 4 1 -2 >
56.482
Harrison's comma
59049 / 57344
| -13 10 0 -1 >
50.724
keega
1029 / 1000
| -3 1 -3 3 >
49.492
septimal quarter tone
36 / 35
| 2 2 -1 -1 >
48.770
quarter tone comma

| 49 50 -25 -25 >
19.2595
cloudy
16807 / 16384
| -14 0 0 5 >
44.130
Avicenna, Avicenna's enharmonic diesis
525 / 512
| -9 1 2 1 >
43.408
slendro diesis
49 / 48
| -4 -1 0 2 >
35.597
slendro 34-comma

| -137 -34 0 68 >
13.692
34-jubilismic comma

| -33 0 -68 68 >
10.829
tritonic diesis, jubilisma
50 / 49
| 1 0 2 -2 >
34.976
eric

| 7 8 0 -7 >
33.859
senga
686 / 675
| 1 -3 -2 3 >
27.985
septimal comma, Archytas' comma, Leipziger Komma
64 / 63
| 6 -2 0 -1 >
27.264
blackjackisma

| -10 7 8 -7 >
22.413
squalentine
64827 / 64000
| -9 3 -3 4 >
22.227
keema
875 / 864
| -5 -3 3 1 >
21.902
gariboh
3125 / 3087
| 0 -2 5 -3 >
21.181
nuwell
2430 / 2401
| 1 5 1 -4 >
20.785
tolerma

| 10 -11 2 1 >
19.948
mirwomo
33075 / 32768
| -15 3 2 2 >
16.144
trimyna
50421 / 50000
| -4 1 -5 5 >
14.516
sensamagic
245 / 243
| 0 -5 1 2 >
14.191
septimal semicomma, starling comma
126 / 125
| 1 2 -3 1 >
13.795
octagar
4000 / 3969
| 5 -4 3 -2 >
13.469
orwellisma, orwell comma
1728 / 1715
| 6 3 -1 -3 >
13.074
quince

| -15 0 -2 7 >
9.154
gamelisma
1029 / 1024
| -10 1 0 3 >
8.433
varunisma

| -9 8 -4 2 >
8.037
septimal kleisma, marvel comma
225 / 224
| -5 2 2 -1 >
7.712
dimcomp

| -1 -4 8 -4 >
7.386
cataharry
19683 / 19600
| -4 9 -2 -2 >
7.316
mirkwai
16875 / 16807
| 0 3 4 -5 >
6.990
stearnsma

| 1 10 0 -6 >
6.595
hemimage
10976 / 10935
| 5 -7 -1 3 >
6.479
hemimean
3136 / 3125
| 6 0 -5 2 >
6.083
hemifamity
5120 / 5103
| 10 -6 1 -1 >
5.758
linus

| 11 -10 -10 10 >
5.572
porwell
6144 / 6125
| 11 1 -3 -2 >
5.362
garischisma

| 25 -14 0 -1 >
3.804
wadisma

| -26 -1 1 9 >
3.792
quasiorwellisma

| 22 -1 -10 1 >
3.734
218edo (stacked 7/4 and 10/9) comma

| 22 -32 16 -3 >
11.982
bapbo
256 / 245
| 8 0 -1 -2 >
76.034

11-limit commas

name(s)
ratio
monzo
cents
11-cycle chroma, 11-11-comma

| -38 0 0 0 11 >
64.497
11-cycle major seventh prote, 35-11-comma

| -121 0 0 0 35 >
96.128
Hunt 11-cycle comma

| -83 0 0 0 24 >
31.631
Hunt flat 5 comma
8192 / 8019
| 13 -6 0 0 -1 >
36.952
sterno
352 / 343
| 5 0 0 -3 1 >
44.840
the Igs boson, 13-11-comma

| 45 0 0 0 -13 >
32.867
telepathma
55 / 54
| -1 -3 1 0 1 >
31.767
thuja comma

| 15 0 1 0 -5 >
29.724
sensmus
1232 / 1215
| 4 -5 -1 1 1 >
24.055
sevnothrush
3168 / 3125
| 5 2 -5 0 1 >
23.659
cassacot
245 / 242
| -1 0 1 2 -2 >
21.330
mothwellsma
99 / 98
| -1 2 0 -2 1 >
17.576
ptolemisma
100 / 99
| 2 -2 2 0 -1 >
17.399
hemimin
1344 / 1331
| 6 1 0 1 -3 >
16.827
biyatisma
121 / 120
| -3 -1 -1 0 2 >
14.367
aphrowe
1331 / 1323
| 0 -3 0 -2 3 >
10.437
valinorsma
176 / 175
| 4 0 -2 -1 1 >
9.865
pentacircle
896 / 891
| 7 -4 0 1 -1 >
9.688
orgonisma
65536 / 65219
| 16 0 0 -2 -3 >
8.394
rastma
243 / 242
| -1 5 0 0 -2 >
7.139
myhemiwell
3388 / 3375
| 2 -3 -3 1 2 >
6.656
keenanisma
385 / 384
| -7 -1 1 1 1 >
4.503
werckisma
441 / 440
| -3 2 -1 2 -1 >
3.930
moctdel
1375 / 1372
| -2 0 3 -3 1 >
3.781

13-limit commas

name(s)
ratio
monzo
cents
Hunt 13-cycle comma

| -37 0 0 0 0 0 10 >
5.277
silver half cents comma

| -8881 0 0 0 2400 >
66.389
Hunt minor submediant comma
1053 / 1024
| -10 4 0 0 0 0 1 >
48.348
astburyp

| -19 -2 0 0 0 6 >
39.255
wilsorma
65 / 64
| -6 0 1 0 0 1 >
26.841
winmeanma
66 / 65
| 1 1 -1 0 1 -1 >
26.432
negustma
78 / 77
| 1 1 0 -1 -1 1 >
22.229
superleap
91 / 90
| -1 -2 -1 1 0 1 >
19.130
animist
105 / 104
| -3 1 1 1 0 -1 >
16.567
secorian
28672 / 28431
| 12 -7 0 1 0 -1 >
14.613
mosaic
3159 / 3136
|-6 5 0 -2 0 1>
12.651
gassorma
275 / 273
| 0 -1 2 -1 1 -1 >
12.637
grossma
144 / 143
| 4 2 0 0 -1 -1 >
12.064
buzurgisma, dhanvantarisma
169 / 168
| -3 -1 0 -1 0 2 >
10.274
catadictma
1287 / 1280
| -8 2 -1 0 1 1 >
9.442
mynucuma
196 / 195
| 2 -1 -1 2 0 -1 >
8.855
huntma
640 / 637
| 7 0 1 -2 0 -1 >
8.134
threedie
2197 / 2187
| 0 -7 0 0 0 3 >
7.897
kestrel comma
1188 / 1183
| 2 3 0 -1 1 -2 >
7.302
marveltwin
325 / 324
| -2 -4 2 0 0 1 >
5.335
ratwolfsma
351 / 350
| -1 3 -2 -1 0 1 >
4.939
minthma
352 / 351
| 5 -3 0 0 1 -1 >
4.925
gentle comma
364 / 363
| 2 -1 0 1 -2 1 >
4.763
cuthbert
847 / 845
| 0 0 -1 1 2 -2 >
4.093

17-limit commas

name(s)
ratio
monzo
cents
11 semitone comma

| 45 0 0 0 0 0 -11 >
45.4905
12 semitone comma

| -49 0 0 0 0 0 12 >
59.465
23 semitone comma

| -93 0 0 0 0 0 23 >
13.974
Hunt 17-cycle comma

| -138 0 0 0 0 0 34 >
31.516
17-ripple integer cents comma

| 327 0 0 0 0 0 -80 >
3.568
Hunt flat 2 comma
4131 / 4096
| -12 5 0 0 0 0 1 >
14.730
Blume comma
2057 / 2048
| -11 0 0 0 2 0 1 >
7.591
Septendecimal Integer Cents comma
289 / 288
| -5 -2 0 0 0 0 2 >
6.001

19-limit commas

name(s)
ratio
monzo
cents
Hunt 19-cycle comma

| 17 0 0 0 0 0 0 -4 >
9.950
spleen comma
210 / 209
| 1 1 1 1 -1 0 0 -1 >
8.264
go comma
361 / 360
| -3 -2 -1 0 0 0 0 2 >
4.802